Twist grain boundaries in three-dimensional lamellar Turing structures

Steady spatial self-organization of three-dimensional chemical reaction-diffusion systems is discussed with the emphasis put on the possible defects that may alter the Turing patterns. It is shown that one of the stable defects of a three-dimensional lamellar Turing structure is a twist grain boundary embedding a Scherk minimal surface.

Pax6 is essential for establishing ventral-dorsal cell boundaries in pituitary gland development

Pax6, a highly conserved member of the paired homeodomain transcription factor family that plays essential roles in ocular, neural, and pancreatic development and effects asymmetric transient dorsal expression during pituitary development, with its expression extinguished before the ventral → dorsal appearance of specific cell types. Analysis of pituitary development in the Small eye and Pax6 −/− mouse mutants reveals that the dorsoventral axis of the pituitary gland becomes ventralized, with dorsal extension of the transcriptional determinants of ventral cell types, particularly PFrk. This ventralization is followed by a marked decrease in terminally differentiated dorsal somatotrope and lactotrope cell types and a marked increase in the expression of markers of the ventral thyrotrope cells and SF-1-expressing cells of gonadotrope lineage. We suggest that the transient dorsal expression of Pax6 is essential for establishing a sharp boundary between dorsal and ventral cell types, based on the inhibition of Shh ventral signals.

Intron positions correlate with module boundaries in ancient proteins

We analyze the three-dimensional structure of proteins by a computer program that finds regions of sequence that contain module boundaries, defining a module as a segment of polypeptide chain bounded in space by a specific given distance. The program defines a set of “linker regions” that have the property that if an intron were to be placed into each linker region, the protein would be dissected into a set of modules all less than the specified diameter. We test a set of 32 proteins, all of ancient origin, and a corresponding set of 570 intron positions, to ask if there is a statistically significant excess of intron positions within the linker regions. For 28-Å modules, a standard size used historically, we find such an excess, with P < 0.003. This correlation is neither due to a compositional or sequence bias in the linker regions nor to a surface bias in intron positions. Furthermore, a subset of 20 introns, which can be putatively identified as old, lies even more explicitly within the linker regions, with P < 0.0003. Thus, there is a strong correlation between intron positions and three-dimensional structural elements of ancient proteins as expected by the introns-early approach. We then study a range of module diameters and show that, as the diameter varies, significant peaks of correlation appear for module diameters centered at 21.7, 27.6, and 32.9 Å. These preferred module diameters roughly correspond to predicted exon sizes of 15, 22, and 30 residues. Thus, there are significant correlations between introns, modules, and a quantized pattern of the lengths of polypeptide chains, which is the prediction of the “Exon Theory of Genes.”

Flows of knowledge from universities and federal laboratories: Modeling the flow of patent citations over time and across institutional and geographic boundaries

The extent to which new technological knowledge flows across institutional and national boundaries is a question of great importance for public policy and the modeling of economic growth. In this paper we develop a model of the process generating subsequent citations to patents as a lens for viewing knowledge diffusion. We find that the probability of patent citation over time after a patent is granted fits well to a double-exponential function that can be interpreted as the mixture of diffusion and obsolescense functions. The results indicate that diffusion is geographically localized. Controlling for other factors, within-country citations are more numerous and come more quickly than those that cross country boundaries.

Molecular genetics of pattern formation in the inner ear: Do compartment boundaries play a role?

The membranous labyrinth of the inner ear establishes a precise geometrical topology so that it may subserve the functions of hearing and balance. How this geometry arises from a simple ectodermal placode is under active investigation. The placode invaginates to form the otic cup, which deepens before pinching off to form the otic vesicle. By the vesicle stage many genes expressed in the developing ear have assumed broad, asymmetrical expression domains. We have been exploring the possibility that these domains may reflect developmental compartments that are instrumental in specifying the location and identity of different parts of the ear. The boundaries between compartments are proposed to be the site of inductive interactions required for this specification. Our work has shown that sensory organs and the endolymphatic duct each arise near the boundaries of broader gene expression domains, lending support to this idea. A further prediction of the model, that the compartment boundaries will also represent lineage-restriction compartments, is supported in part by fate mapping the otic cup. Our data suggest that two lineage-restriction boundaries intersect at the dorsal pole of the otocyst, a convergence that may be critical for the specification of endolymphatic duct outgrowth. We speculate that the patterning information necessary to establish these two orthogonal boundaries may emanate, in part, from the hindbrain. The compartment boundary model of ear development now needs to be tested through a variety of experimental perturbations, such as the removal of boundaries, the generation of ectopic boundaries, and/or changes in compartment identity.